# Hyperboloid of One Sheet

The hyperboloid Of One Sheet is a surface of revolution of the curve family hyperbola.

The parametric formula for the Hyperboloid of One Sheet is:

ParametricPlot3D[{Cosh[u]*Cos[v], Cosh[u]*Sin[v], Sinh[u]}, {u, -2, 2}, {v, 0, 2*π}] (* u → height, v → circular sweep. *)

### Ruled Surface

A revolving around its transverse axis forms a surface called “hyperboloid of one sheet”. A hyperboloid is a Ruled Surface.

Ruled surfaces are surfaces that for every point on the surface, there is a line on the surface passing it. Or, in other words, a surface generated by a line. If for each point on the surface there are two lines on the surface passing it, then it's called doubly-ruled surface. Hyperboloid is a doubly-ruled surface.

Ruled surfaces also include cylinder and helicoid. There are only 3 doubly ruled surfaces: The hyperboloid, hyperbolic paraboloid, and plane.

#### Spinning Cube Silhouette

The silhouette of a rotating dice is a hyperbola.

### Hyperboloid in Architecture

Due to its simplicity and beauty, the hyperboloid is often used in architecture for towers. They are called Hyperboloid structure.

For more photos, see: Hyperboloid Towers.

Other algebaric surfaces that has cross-sections of conic sections are: ellipsoid, paraboloid, hyperbolic paraboloid, hyperboloid of one sheet, hyperboloid of two sheets.

If you have a question, put $5 at patreon and message me.